Movie Rating Model and Predictor

Part 1: Data

The data were comprised of audience and critics opinions, awards, studio, and actor information from Rotten Tomatoes, imdb, and BoxOfficeMojo.com for a random sample of 651 movies produced and released prior to 2016.

Data Sources

Rotten Tomatoes

Launched in August 1998 by Senh Duong, Rotten Tomatoes is an American review aggregation website for film and television.

IMDB

Generalizability

Selected Features

The full codebook for the data set can be found in Appendix A. Table 1 lists the data variables selected from the raw data that were included at this stage in this study.
Table 1: Selected features
Type Variable Description
Overview
Categorical title_type Type of movie (Documentary, Feature Film, TV Movie)
Categorical genre Genre of movie (Action & Adventure, Comedy, Documentary, Drama, Horror, Mystery & Suspense, Other)
Numeric runtime Runtime of movie (in minutes)
Categorical mpaa_rating MPAA rating of the movie (G, PG, PG-13, R, Unrated)
Organization
Categorical studio Studio that produced the movie
Categorical director Director of the movie
Dates
Categorical thtr_rel_month Month the movie is released in theaters
Performance
Numeric imdb_num_votes Number of votes on IMDB
Numeric imdb_num_votes_log Log number of IMDB votes
Numeric imdb_rating Rating on IMDB
Numeric critics_score Critics score on Rotten Tomatoes
Numeric audience_score Audience score on Rotten Tomatoes
Categorical best_pic_nom Whether or not the movie was nominated for a best picture Oscar (no, yes)
Categorical best_pic_win Whether or not the movie won a best picture Oscar (no, yes)
Categorical best_actor_win Whether or not one of the main actors in the movie ever won an Oscar (no, yes) – note that this is not necessarily whether the actor won an Oscar for their role in the given movie
Categorical best_actress_win Whether or not one of the main actresses in the movie ever won an Oscar (no, yes) – not that this is not necessarily whether the actresses won an Oscar for their role in the given movie
Categorical best_dir_win Whether or not the director of the movie ever won an Oscar (no, yes) – not that this is not necessarily whether the director won an Oscar for the given movie
Categorical top200_box Whether or not the movie is in the Top 200 Box Office list on BoxOfficeMojo (no, yes)
Box Office
Numeric box_office Box office revenue from BoxOfficeMojo.com
Numeric box_office_log Log of Box office revenue from BoxOfficeMojo.com

Note that the values for the box office variables were obtained for a random sample of 100 reviews from the BoxOfficeMojo.com website.

Derived Features

The following additional features (Table 2) were derived from selected features and are as follows:
Table 2: Derived features
Type Variable Description
Dates
Categorical thtr_rel_season Season the movie was released in theaters
Experience
Numeric director_experience Total number of films in sample for a director
Numeric cast_experience The sum across all cast members for a film, of the number of films in which each actor appeared
Performance
Numeric cast_votes Total number of allocated IMDB votes for the cast of a film
Numeric cast_votes_log Log of the total number of allocated IMDB votes for the cast of a film
Interaction
Numeric scores 10 * IMDB Rating + critics score + audience_score
Numeric scores_log Log(10 * IMDB Rating + critics score + audience_score)
Numeric votes_imdb_rating Votes * imdb_rating
Numeric votes_imdb_rating_log log(votes * imdb_rating)
Numeric votes_critics_score votes * critics_score
Numeric votes_critics_score_log log(votes * critics_score)
Numeric votes_audience_score votes * audience_score
Numeric votes_audience_score_log log(votes * audience_score)
Numeric votes_scores votes * scores
Numeric votes_scores_log log(votes * scores)

Cast experience and cast votes for each film were computed as follows:
Cast Experience
Cast experience for each film was defined by:
\[e = \displaystyle\sum_{i=1}^{5} N_i\] where:
\(e\) is the total cast experience for the film
\(N_i\) is the total number of films in which actor \(i\) was involved

Cast Votes Cast votes for each film was defined by:
\[v = \displaystyle\sum_{i=1}^{5} V_i\] where:
\(v\) is the sum of IMDB cast votes for the film
\(V_i\) is the sum of allocated IMDB cast votes for actor \(i\)

imdb votes were allocated to cast members as follows:
* 40% of total film IMDB votes for actor1
* 30% of total film IMDB votes for actor2
* 15% of total film IMDB votes for actor3
* 10% of total film IMDB votes for actor4
* 5% of total film IMDB votes for actor5

Each actor was allocated points accordingly, then the votes were aggregated for each film in which the cast member appeared. The IMDB votes were counted without regard for date to compensate for the limitations imposed by the sample size as movegoers had access to the population of reviews and director, studio, and actor performance data when making their purchase decision.

Omitted Features

The features listed in Table 3 were not included for redundancy reasons or due to the lack of direct relevance to the research question. Some variables, such as the actor variables, were used to derive other variables which are further described below.

Table 3: Omitted features
Variable Description
title Title of movie
imdb_url Link to IMDB page for the movie
rt_url Link to Rotten Tomatoes page for the movie
actor1 First main actor/actress in the abridged cast of the movie
actor2 Second main actor/actress in the abridged cast of the movie
actor3 Third main actor/actress in the abridged cast of the movie
actor4 Fourth main actor/actress in the abridged cast of the movie
actor5 Fifth main actor/actress in the abridged cast of the movie
thtr_rel_year Year the movie is released in theaters
thtr_rel_day Day of the month the movie is released in theaters
dvd_rel_year Year the movie is released on DVD
dvd_rel_month Month the movie is released on DVD
dvd_rel_day Day of the month the movie is released on DVD
critics_rating Categorical variable for critics rating on Rotten Tomatoes (Certified Fresh, Fresh, Rotten)
audience_rating Categorical variable for audience rating on Rotten Tomatoes (Spilled, Upright)

Data Cleaning

The variables of interest were obtained from the data and complete cases were extracted reducing the number of observations from 651 to 623.


Part 2: Research question

The underlying intent of this analysis was to determine the factors that most influence box office success for a film. Since box office revenue was not among the variables included in the raw data set, the first task was to determine which of the selected (or derived) variables would stand as a proxy for box office success. As such the first research question is concretely stated as follows:
> Which of the selected or derived variables is most highly associated / correlated with total lifetime box office revenue

Once this proxy response variable was determined, the features that are most highly associated / correlated with this response variable were examined via the following research question.
> Which features are most highly associated / correlated with the proxy response for box office success


Part 3: Exploratory data analysis

The exploratory data analysis began with a data preprocessing step to extract complete cases, and to create the response and two additional explanatory variables. Next, a univariate analysis examined each variable on a univariate basis. Lastly, a bivariate analysis explored the relationships between the response variable and various candidate predictors.

Univariate Analysis

Univariate Analysis of Categorical Variables

The purpose of the univariate analysis of categorical variables was to examine the relative frequencies and proportions of observations for each level of the categorical level. Categorical levels with fewer than five observations were removed from further analysis.

The categorical variables included at this stage of the analysis are indicated in Table 4.

Table 4: Categorical Variables
Variable Description
thtr_rel_season Season the movie was released in theaters
title_type Type of movie (Documentary, Feature Film, TV Movie)
genre Genre of movie (Action & Adventure, Comedy, Documentary, Drama, Horror, Mystery & Suspense, Other)
mpaa_rating MPAA rating of the movie (G, PG, PG-13, R, Unrated)
studio Studio that produced the movie
director Director of the movie
thtr_rel_month Month the movie is released in theaters
best_pic_nom Whether or not the movie was nominated for a best picture Oscar (no, yes)
best_pic_win Whether or not the movie won a best picture Oscar (no, yes)
best_actor_win Whether or not one of the main actors in the movie ever won an Oscar (no, yes) – note that this is not necessarily whether the actor won an Oscar for their role in the given movie
best_actress_win Whether or not one of the main actresses in the movie ever won an Oscar (no, yes) – not that this is not necessarily whether the actresses won an Oscar for their role in the given movie
best_dir_win Whether or not the director of the movie ever won an Oscar (no, yes) – not that this is not necessarily whether the director won an Oscar for the given movie
top200_box Whether or not the movie is in the Top 200 Box Office list on BoxOfficeMojo (no, yes)

Title Type

Feature films constituted 92% of the films in the sample. Since the focus of this study was theatrical releases, TV movies, which were included in the raw data were excluded from this analysis.

Figure 1: Films by title type

Genre

The drama genre represented a plurality of the releases in the sample, followed by comedy action & adventure then mystery & suspense. The top four genres account for nearly 80% of the films in the sample. Figure 2: Films by genre

MPAA Rating

Rated R films accounted for over 0% of the releases, followed by PG and PG-13. Collectively, R, PG, and PG-13 rated films represent 90% of the films in the sample. NC-17 films were excluded from this analysis. Figure 3: Films by MPAA Rating

Studio

The data included films from 200 studios. Data with respect to the number of films in the sample per studio are captured in the studio experience variable below.

Director

The work of 507 directors was included in the sample provided for this project. Data with respect to the number of films in the sample per director are captured in the director experience variable below.

Season of Theatrical Release

The plurality of features in the sample were released during the fall and summer months with over 20% opening in the month of December alone. Figure 4: Theatrical releases by season

Month of Theatrical Release

The plurality of features in the sample (31%) were released during the months of January, June, October and December.
Figure 5: Theatrical releases by month

Best Picture

Since the proportion of films nominated for and winning best picture were so small, this variable was not likely to be a good predictor of movie popularity. The bivariate analysis below will illuminate this further.

Figure 6: Best picture nominations and wins

Best Director / Actor / Actress

As indicated in Figure 7, the percentages of films with best director, actor and actress oscars were 7%, 15%, and 11%, respectively. Again, these proportions indicate that oscar awards would not be a good predictor of movie popularity. The bivariate analysis will explore this further.

Figure 7: Best director/actor/actress

Top 200 Box Office

Again, the proportion of films in the Top 200 Box Office list was miniscule indicating that inclusion in the top 200 box office list was not likely to be a good predictor of movie popularity. Figure 8: Frequency and proportion of movies by top 200 box office earnings

Univariate Analysis of Quantitative Variables

The primary aim of this analysis was to examine the distribution of the variables vis-a-vis a normal distribution, and to identify potential outliers. Summary statistics, histograms, boxplots, normal quantile-quantile plots were rendered for each variable. The quantitative variables included at this stage of the analysis are indicated in Table 5.

Table 5: Quantitative Variables
Variable Description
director_experience Total number of films in sample for a director
cast_experience The sum across all cast members for a film, of the number of films in which each actor appeared
cast_votes Total number of allocated IMDB votes for the cast of a film
cast_votes_log Log of the total number of allocated IMDB votes for the cast of a film
scores 10 * IMDB Rating + critics score + audience_score
scores_log Log(10 * IMDB Rating + critics score + audience_score)
votes_imdb_rating Votes * imdb_rating
votes_imdb_rating_log log(votes * imdb_rating)
votes_critics_score votes * critics_score
votes_critics_score_log log(votes * critics_score)
votes_audience_score votes * audience_score
votes_audience_score_log log(votes * audience_score)
votes_scores votes * scores
votes_scores_log log(votes * scores)
runtime Runtime of movie (in minutes)
imdb_num_votes Number of votes on IMDB
imdb_num_votes_log Log number of IMDB votes
imdb_rating Rating on IMDB
critics_score Critics score on Rotten Tomatoes
audience_score Audience score on Rotten Tomatoes
box_office Box office revenue from BoxOfficeMojo.com
box_office_log Log of Box office revenue from BoxOfficeMojo.com

Director Experience

This derived variable measured the relative experience of a given director and was defined as the sum of the observations for the director associated with each film.

Table 6: Director experience summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 1 1 1 1.5 2 1 4 0 0.75 51.2 2.57 1.73

Figure 9: Director experience histogram and QQ Plot

Figure 10: Director experience boxplot

Central Tendency: The summary statistics (Table 6) the central tendency for director experience was 1 films and 1.5 films for the median and mean, respectively.

Dispersion: The standard deviation, s = 0.75, corresponds with a coefficient of variation of 51.2%, indicating a high degree of dispersion.

Shape of Distribution: The sample skewness (1.73), indicated that the distribution of director experience was right-skewed. The sample kurtosis (2.57), indicated that the distribution of director experience was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 9 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 10, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 1, 2, and 1, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 3.5]. Indeed, this confirmed the existence of 20 outliers. Given the proximity of the outliers to the 1.5xIQR, no effort was made to remove them.

Cast Experience

This derived variable measured the relative experience of a given cast and was defined as the sum of the observations for the cast associated with each film.

Table 7: Cast experience summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 5 6 7 7.5 9 3 15 0 2.16 29 0.33 0.89

Figure 11: Cast experience histogram and QQ Plot

Figure 12: Cast experience boxplot

Central Tendency: The summary statistics (Table 7) the central tendency for cast experience was 7 films and 7.5 films for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.16, corresponds with a coefficient of variation of 29%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (0.89), indicated that the distribution of cast experience was right-skewed. The sample kurtosis (0.33), indicated that the distribution of cast experience was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 11 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 12, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 6, 9, and 3, respectively. This yielded a 1.5xIQR ‘acceptable’ range [1.5, 13.5]. Indeed, this confirmed the existence of 7 outliers. Given the proximity of the outliers to the 1.5xIQR, no effort was made to remove them.

Number of IMDB Votes

This variable captured the number of IMDB votes cast for each film.

Table 8: IMDB votes summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 183 4986 15806 59291.3 60409 55423 893008 0 113763.6 191.9 19.43 3.99

Figure 13: IMDB votes histogram and QQ Plot

Figure 14: IMDB votes boxplot

Central Tendency: The summary statistics (Table 8) the central tendency for imdb votes was 15,806 votes and 59,291.3 votes for the median and mean, respectively.

Dispersion: The standard deviation, s = 113,763.58, corresponds with a coefficient of variation of 191.9%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (3.99), indicated that the distribution of imdb votes was right-skewed. The sample kurtosis (19.43), indicated that the distribution of imdb votes was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 13 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 14, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 4,986, 60,409, and 55,423, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 143,543.5]. Indeed, this confirmed the existence of 68 outliers.

Log Number of IMDB Votes

This was a log transformation of the IMDB votes variable.

Table 9: Log IMDB votes summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 7.5 12.3 13.9 14.1 15.9 3.6 19.8 0 2.37 16.8 -0.57 0.04

Figure 15: Log IMDB votes histogram and QQ Plot

Figure 16: Log IMDB votes boxplot

Central Tendency: The summary statistics (Table 9) the central tendency for imdb log votes was 13.9 log votes and 14.1 log votes for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.37, corresponds with a coefficient of variation of 16.8%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (0.04), indicated that the distribution of imdb log votes was approximately symmetric. The sample kurtosis (-0.57), indicated that the distribution of imdb log votes was platykurtic or light-tailed. The histogram and QQ plot in Figure 15 reveal a nearly normal distribution.

Outliers: The boxplot in Figure 16, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 12.3, 15.9, and 3.6, respectively. This yielded a 1.5xIQR ‘acceptable’ range [6.9, 21.3]. Indeed, this confirmed the existence of no outliers.

IMDB Ratings

This variable captured the IMDB rating for each film

Table 10: IMDB rating summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 1.9 5.9 6.6 6.5 7.3 1.4 9 0 1.09 16.8 1.27 -0.89

Figure 17: IMDB rating histogram and QQ Plot

Figure 18: IMDB rating boxplot

Central Tendency: The summary statistics (Table 10) the central tendency for imdb rating was 6.6 points and 6.5 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 1.09, corresponds with a coefficient of variation of 16.8%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-0.89), indicated that the distribution of imdb rating was left-skewed. The sample kurtosis (1.27), indicated that the distribution of imdb rating was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 17 reveal a nearly normal distribution.

Outliers: The boxplot in Figure 18, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 5.9, 7.3, and 1.4, respectively. This yielded a 1.5xIQR ‘acceptable’ range [3.8, 9.4]. Indeed, this confirmed the existence of 19 outliers.

Critics Scores

This variable captured the critics scores for each film

Table 11: Critics score summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 1 33 61 57.2 82 49 100 0 28.38 49.6 -1.18 -0.25

Figure 19: Critics score histogram and QQ Plot

Figure 20: Critics score boxplot

Central Tendency: The summary statistics (Table 11) the central tendency for critics score was 61 points and 57.2 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 28.38, corresponds with a coefficient of variation of 49.6%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (-0.25), indicated that the distribution of critics score was approximately symmetric. The sample kurtosis (-1.18), indicated that the distribution of critics score was platykurtic or light-tailed. The histogram and QQ plot in Figure 19 reveals a left skewed distribution that departs from normality.

Outliers: The boxplot in Figure 20, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 33, 82, and 49, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 155.5]. Indeed, this confirmed the existence of no outliers.

Audience Scores

This variable captured the audience scores for each film

Table 12: Audience score summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 1 33 61 57.2 82 49 100 0 28.38 49.6 -1.18 -0.25

Figure 21: Audience score histogram and QQ Plot

Figure 22: Audience score boxplot

Central Tendency: The summary statistics (Table 12) the central tendency for audience score was 61 points and 57.2 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 28.38, corresponds with a coefficient of variation of 49.6%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (-0.25), indicated that the distribution of audience score was approximately symmetric. The sample kurtosis (-1.18), indicated that the distribution of audience score was platykurtic or light-tailed. The histogram and QQ plot in Figure 21 reveals a left skewed distribution that departs from normality.

Outliers: The boxplot in Figure 22, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 33, 82, and 49, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 155.5]. Indeed, this confirmed the existence of no outliers.

Studio Votes

This variable captured the studio votes for each film

Table 13: Studio votes summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 183 50390.5 250669 903089.8 790665 740274.5 4404677 0 1347877 149.3 1.3 1.64

Figure 23: Studio votes histogram and QQ Plot

Figure 24: Studio votes boxplot

Central Tendency: The summary statistics (Table 13) the central tendency for studio votes was 250,669 votes and 903,089.8 votes for the median and mean, respectively.

Dispersion: The standard deviation, s = 1,347,877.47, corresponds with a coefficient of variation of 149.3%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (1.64), indicated that the distribution of studio votes was right-skewed. The sample kurtosis (1.3), indicated that the distribution of studio votes was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 23 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 24, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 50,390.5, 790,665, and 740,274.5, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 1,901,076.75]. Indeed, this confirmed the existence of 126 outliers.

Log Studio Votes

This is a log transformation of the studio votes variable.

Table 14: Log studio votes summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 7.5 15.6 17.9 17.5 19.6 4 22.1 0 3.23 18.5 -0.53 -0.5

Figure 25: Log studio votes histogram and QQ Plot

Figure 26: Log studio votes boxplot

Central Tendency: The summary statistics (Table 14) the central tendency for log studio votes was 17.9 log(votes) and 17.5 log(votes) for the median and mean, respectively.

Dispersion: The standard deviation, s = 3.23, corresponds with a coefficient of variation of 18.5%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-0.5), indicated that the distribution of log studio votes was approximately symmetric. The sample kurtosis (-0.53), indicated that the distribution of log studio votes was platykurtic or light-tailed. The histogram and QQ plot in Figure 25 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 26, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 15.6, 19.6, and 4, respectively. This yielded a 1.5xIQR ‘acceptable’ range [9.6, 25.6]. Indeed, this confirmed the existence of 3 outliers.

Cast Votes

This variable captured the total number of votes allocated to each cast member for a film.

Table 15: Cast votes summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 183 17866 76506.8 156740.5 226478.2 208612.2 1504872 0 197381.9 125.9 6.65 2.18

Figure 27: Cast votes histogram and QQ Plot

Figure 28: Cast votes boxplot

Central Tendency: The summary statistics (Table 15) the central tendency for cast votes was 76,506.8 votes and 156,740.5 votes for the median and mean, respectively.

Dispersion: The standard deviation, s = 197,381.94, corresponds with a coefficient of variation of 125.9%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (2.18), indicated that the distribution of cast votes was right-skewed. The sample kurtosis (6.65), indicated that the distribution of cast votes was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 27 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 28, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 17,866, 226,478.2, and 208,612.2, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 539,396.5]. Indeed, this confirmed the existence of 28 outliers.

Log Cast Votes

This is a log transformation of the cast votes variable.

Table 16: Log cast votes summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 7.5 14.1 16.2 15.8 17.8 3.7 20.5 0 2.47 15.6 -0.15 -0.63

Figure 29: Log cast votes histogram and QQ Plot

Figure 30: Log cast votes boxplot

Central Tendency: The summary statistics (Table 16) the central tendency for log cast votes was 16.2 log(votes) and 15.8 log(votes) for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.47, corresponds with a coefficient of variation of 15.6%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-0.63), indicated that the distribution of log cast votes was left-skewed. The sample kurtosis (-0.15), indicated that the distribution of log cast votes was platykurtic or light-tailed. The histogram and QQ plot in Figure 29 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 30, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 14.1, 17.8, and 3.7, respectively. This yielded a 1.5xIQR ‘acceptable’ range [8.55, 23.35]. Indeed, this confirmed the existence of 3 outliers.

Scores

This variable captured the total score for each film defined as 10 * IMDB Rating + critics score + audience_score.

Table 11Table 12Table 17: Scores summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 38 144.5 185 184.1 231.5 87 284 0 54.75 29.7 -0.82 -0.32

Figure 19Figure 21Figure 31: Scores histogram and QQ Plot

Figure 20Figure 22Figure 32: Scores boxplot

Central Tendency: The summary statistics (Table 11Table 12Table 17) the central tendency for total scores was 185 points and 184.1 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 54.75, corresponds with a coefficient of variation of 29.7%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (-0.32), indicated that the distribution of total scores was approximately symmetric. The sample kurtosis (-0.82), indicated that the distribution of total scores was platykurtic or light-tailed. The histogram and QQ plot in Figure 19Figure 21Figure 31 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 20Figure 22Figure 32, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 144.5, 231.5, and 87, respectively. This yielded a 1.5xIQR ‘acceptable’ range [14, 362]. Indeed, this confirmed the existence of no outliers.

Log Scores

This is a log transformation of scores variable.

Table 18: Log scores summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 5.2 7.2 7.5 7.4 7.9 0.7 8.1 0 0.5 6.7 1.12 -1.07

Figure 33: Log scores histogram and QQ Plot

Figure 34: Log scores boxplot

Central Tendency: The summary statistics (Table 18) the central tendency for log total scores was 7.5 points and 7.4 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 0.5, corresponds with a coefficient of variation of 6.7%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-1.07), indicated that the distribution of log total scores was left-skewed. The sample kurtosis (1.12), indicated that the distribution of log total scores was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 33 reveals a left skewed distribution that departs rather significantly from normality.

Outliers: The boxplot in Figure 34, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 7.2, 7.9, and 0.7, respectively. This yielded a 1.5xIQR ‘acceptable’ range [6.15, 8.95]. Indeed, this confirmed the existence of 14 outliers.

IMDB Votes * Rating

This interaction variable is defined as the product of IMDB votes and IMDB ratings.

Table 19: IMDB Votes * Rating summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 1335.9 30708.1 99088.8 426584.5 391389.5 360681.5 7590568 0 910840.8 213.5 24.2 4.47

Figure 35: IMDB Votes * Rating histogram and QQ Plot

Figure 36: IMDB Votes * Rating votes boxplot

Central Tendency: The summary statistics (Table 19) the central tendency for votes * imdb rating was 99,088.8 points and 426,584.5 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 910,840.83, corresponds with a coefficient of variation of 213.5%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (4.47), indicated that the distribution of votes * imdb rating was right-skewed. The sample kurtosis (24.2), indicated that the distribution of votes * imdb rating was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 35 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 36, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 30,708.1, 391,389.5, and 360,681.5, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 932,411.75]. Indeed, this confirmed the existence of 73 outliers.

Log IMDB Votes * Rating

This is a log transformation of IMDB Votes * Rating variable.

Table 20: Log IMDB Votes * Rating summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 10.4 14.9 16.6 16.8 18.6 3.7 22.9 0 2.44 14.6 -0.56 0.13

Figure 37: Log IMDB Votes * Rating histogram and QQ Plot

Figure 38: Log IMDB Votes * Rating boxplot

Central Tendency: The summary statistics (Table 20) the central tendency for log(votes * imdb rating) was 16.6 log points and 16.8 log points for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.44, corresponds with a coefficient of variation of 14.6%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (0.13), indicated that the distribution of log(votes * imdb rating) was approximately symmetric. The sample kurtosis (-0.56), indicated that the distribution of log(votes * imdb rating) was platykurtic or light-tailed. The histogram and QQ plot in Figure 37 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 38, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 14.9, 18.6, and 3.7, respectively. This yielded a 1.5xIQR ‘acceptable’ range [9.35, 24.15]. Indeed, this confirmed the existence of no outliers.

IMDB Votes * Critics Score

This interaction variable is defined as the product of IMDB votes and critics score.

Table 21: IMDB Votes * Critics Score summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 11310 196248 815572 4111799 3341443 3145195 78584704 0 9677896 235.4 23.77 4.51

Figure 39: IMDB Votes * Critics Score histogram and QQ Plot

Figure 40: IMDB Votes * Critics Score votes boxplot

Central Tendency: The summary statistics (Table 21) the central tendency for votes * critics score was 815,572 points and 4,111,799.3 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 9,677,896.18, corresponds with a coefficient of variation of 235.4%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (4.51), indicated that the distribution of votes * critics score was right-skewed. The sample kurtosis (23.77), indicated that the distribution of votes * critics score was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 39 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 40, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 196,248, 3,341,442.5, and 3,145,194.5, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 8,059,234.25]. Indeed, this confirmed the existence of 83 outliers.

Log IMDB Votes * Critics Score

This is a log transformation of IMDB Votes * Critics Score variable.

Table 22: Log IMDB Votes * Critics Score summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 13.5 17.6 19.6 19.6 21.7 4.1 26.2 0 2.71 13.8 -0.58 0.13

Figure 41: Log IMDB Votes * Critics Score histogram and QQ Plot

Figure 42: Log IMDB Votes * Critics Score boxplot

Central Tendency: The summary statistics (Table 22) the central tendency for log(votes * critics score) was 19.6 log points and 19.6 log points for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.71, corresponds with a coefficient of variation of 13.8%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (0.13), indicated that the distribution of log(votes * critics score) was approximately symmetric. The sample kurtosis (-0.58), indicated that the distribution of log(votes * critics score) was platykurtic or light-tailed. The histogram and QQ plot in Figure 41 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 42, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 17.6, 21.7, and 4.1, respectively. This yielded a 1.5xIQR ‘acceptable’ range [11.45, 27.85]. Indeed, this confirmed the existence of no outliers.

IMDB Votes * Audience Score

This interaction variable is defined as the product of IMDB votes and audience score.

Table 23: IMDB Votes * Audience Score summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 9750 257713.5 859140 4378112 3664785 3407072 81263728 0 9805170 224 24.64 4.53

Figure 43: IMDB Votes * Audience Score histogram and QQ Plot

Figure 44: IMDB Votes * Audience Score votes boxplot

Central Tendency: The summary statistics (Table 23) the central tendency for votes * audience score was 859,140 points and 4,378,111.7 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 9,805,170.02, corresponds with a coefficient of variation of 224%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (4.53), indicated that the distribution of votes * audience score was right-skewed. The sample kurtosis (24.64), indicated that the distribution of votes * audience score was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 43 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 44, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 257,713.5, 3,664,785, and 3,407,071.5, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 8,775,392.25]. Indeed, this confirmed the existence of 80 outliers.

Log IMDB Votes * Audience Score

This is a log transformation of IMDB Votes * Audience Score variable.

Table 24: Log IMDB Votes * Audience Score summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 13.3 18 19.7 20 21.8 3.8 26.3 0 2.54 12.7 -0.58 0.16

Figure 45: Log IMDB Votes * Audience Score histogram and QQ Plot

Figure 46: Log IMDB Votes * Audience Score boxplot

Central Tendency: The summary statistics (Table 24) the central tendency for log(votes * audience score) was 19.7 log points and 20 log points for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.54, corresponds with a coefficient of variation of 12.7%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (0.16), indicated that the distribution of log(votes * audience score) was approximately symmetric. The sample kurtosis (-0.58), indicated that the distribution of log(votes * audience score) was platykurtic or light-tailed. The histogram and QQ plot in Figure 45 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 46, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 18, 21.8, and 3.8, respectively. This yielded a 1.5xIQR ‘acceptable’ range [12.3, 27.5]. Indeed, this confirmed the existence of no outliers.

IMDB Votes * Total Score

This interaction variable is defined as the product of IMDB votes and total score.

Table 25: IMDB Votes * Total Score summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 42822 829162 2699180 12755756 10554420 9725258 235754112 0 28491864 223.4 24.13 4.5

Figure 47: IMDB Votes * Total Score histogram and QQ Plot

Figure 48: IMDB Votes * Total Score votes boxplot

Central Tendency: The summary statistics (Table 25) the central tendency for votes * total score was 2,699,180 points and 12,755,756.4 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 28,491,863.84, corresponds with a coefficient of variation of 223.4%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (4.5), indicated that the distribution of votes * total score was right-skewed. The sample kurtosis (24.13), indicated that the distribution of votes * total score was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 47 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 48, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 829,162, 10,554,419.5, and 9,725,257.5, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 25,142,305.75]. Indeed, this confirmed the existence of 81 outliers.

Log IMDB Votes * Total Score

This is a log transformation of IMDB Votes * Total Score variable.

Table 26: Log IMDB Votes * Total Score summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 15.4 19.7 21.4 21.5 23.3 3.7 27.8 0 2.5 11.6 -0.56 0.18

Figure 49: Log IMDB Votes * Total Score histogram and QQ Plot

Figure 50: Log IMDB Votes * Total Score boxplot

Central Tendency: The summary statistics (Table 26) the central tendency for log(votes * total score) was 21.4 log points and 21.5 log points for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.5, corresponds with a coefficient of variation of 11.6%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (0.18), indicated that the distribution of log(votes * total score) was approximately symmetric. The sample kurtosis (-0.56), indicated that the distribution of log(votes * total score) was platykurtic or light-tailed. The histogram and QQ plot in Figure 49 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 50, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 19.7, 23.3, and 3.7, respectively. This yielded a 1.5xIQR ‘acceptable’ range [14.15, 28.85]. Indeed, this confirmed the existence of no outliers.

Runtime

Total lifetime runtime was obtained for a subset of 100 randomly selected films from the movie data set. This is an analysis of runtime for this random sampling.

Table 27: Runtime summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
627 65 93 103 106.4 116 23 267 0 19.1 17.9 9.61 1.98

Figure 51: Runtime histogram and QQ Plot

Figure 52: Runtime boxplot

Central Tendency: The summary statistics (Table 27) the central tendency for runtime was 103 minutes and 106.4 minutes for the median and mean, respectively.

Dispersion: The standard deviation, s = 19.1, corresponds with a coefficient of variation of 17.9%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (1.98), indicated that the distribution of runtime was right-skewed. The sample kurtosis (9.61), indicated that the distribution of runtime was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 51 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 52, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 93, 116, and 23, respectively. This yielded a 1.5xIQR ‘acceptable’ range [58.5, 150.5]. Indeed, this confirmed the existence of 16 outliers.

Box Office

Total lifetime box office revenue was obtained for a subset of 100 randomly selected films from the movie data set. This is an analysis of box office revenue for this random sampling.

Table 28: Box office revenue summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
232 2749 1046501 13235741 38445478 48596084 47549583 658672302 0 68819864 179 31.3 4.56

Figure 53: Box office revenue histogram and QQ Plot

Figure 54: Box office revenue boxplot

Central Tendency: The summary statistics (Table 28) the central tendency for box office was 13,235,741 dollars and 38,445,478.3 dollars for the median and mean, respectively.

Dispersion: The standard deviation, s = 68,819,863.95, corresponds with a coefficient of variation of 179%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (4.56), indicated that the distribution of box office was right-skewed. The sample kurtosis (31.3), indicated that the distribution of box office was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 53 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 54, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 1,046,501, 48,596,084, and 47,549,583, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 119,920,458.5]. Indeed, this confirmed the existence of 21 outliers.

Log Box Office

This is a log transformation of the box office variable.

Table 29: Log box office revenue summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
232 11.4 20 23.7 22.5 25.5 5.5 29.3 0 3.89 17.3 -0.21 -0.81

Figure 55: Log box office revenue histogram and QQ Plot

Figure 56: Log box office revenue boxplot

Central Tendency: The summary statistics (Table 29) the central tendency for log box office was 23.7 log(dollars) and 22.5 log(dollars) for the median and mean, respectively.

Dispersion: The standard deviation, s = 3.89, corresponds with a coefficient of variation of 17.3%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-0.81), indicated that the distribution of log box office was left-skewed. The sample kurtosis (-0.21), indicated that the distribution of log box office was platykurtic or light-tailed. The histogram and QQ plot in Figure 55 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 56, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 20, 25.5, and 5.5, respectively. This yielded a 1.5xIQR ‘acceptable’ range [11.75, 33.75]. Indeed, this confirmed the existence of 1 outliers.

Bivariate Analysis

The overarching aim was to understand which factors most influenced box office success for a film. Since box office revenue was not among the features provided in the data set, a proxy was selected among the quantitative variables most highly correlated with box office revenue. Courtesy of BoxOfficeMojo, lifetime box office revenue was obtained for a random sampling of 100 films from the data set in order to ascertain which variable most highly correlated with revenue.

Figure 57: Correlation between log box office revenue and explanatory variables
Variable Correlation Statistic df p.value X95..CI
studio_votes_log 0.70 15.04 230 < 0.05 [ 0.63 , 0.76 ]
imdb_num_votes_log 0.69 14.31 230 < 0.05 [ 0.61 , 0.75 ]
votes_imdb_rating_log 0.65 13.07 230 < 0.05 [ 0.57 , 0.72 ]
votes_audience_score_log 0.65 12.88 230 < 0.05 [ 0.57 , 0.72 ]
votes_scores_log 0.63 12.38 230 < 0.05 [ 0.55 , 0.7 ]
cast_votes_log 0.57 10.58 230 < 0.05 [ 0.48 , 0.65 ]
votes_critics_score_log 0.54 9.79 230 < 0.05 [ 0.44 , 0.63 ]
studio_experience_log 0.53 9.50 230 < 0.05 [ 0.43 , 0.62 ]
studio_votes 0.52 9.21 230 < 0.05 [ 0.42 , 0.61 ]
studio_experience 0.47 8.16 230 < 0.05 [ 0.37 , 0.57 ]
imdb_num_votes 0.47 8.05 230 < 0.05 [ 0.36 , 0.56 ]
cast_votes 0.46 7.89 230 < 0.05 [ 0.35 , 0.56 ]
votes_imdb_rating 0.43 7.26 230 < 0.05 [ 0.32 , 0.53 ]
votes_scores 0.42 6.99 230 < 0.05 [ 0.31 , 0.52 ]
votes_audience_score 0.42 6.96 230 < 0.05 [ 0.3 , 0.52 ]
votes_critics_score 0.40 6.65 230 < 0.05 [ 0.29 , 0.5 ]
cast_experience_log 0.40 6.55 230 < 0.05 [ 0.28 , 0.5 ]
cast_experience 0.38 6.13 230 < 0.05 [ 0.26 , 0.48 ]
runtime 0.27 4.27 230 < 0.05 [ 0.15 , 0.39 ]
director_experience_log 0.27 4.25 230 < 0.05 [ 0.15 , 0.39 ]
director_experience 0.25 3.94 230 < 0.05 [ 0.13 , 0.37 ]
critics_score -0.14 -2.09 230 < 0.05 [ -0.26 , -0.01 ]
scores_log -0.10 -1.45 230 0.148 [ -0.22 , 0.03 ]
imdb_rating -0.09 -1.34 230 0.182 [ -0.21 , 0.04 ]
scores -0.09 -1.33 230 0.185 [ -0.21 , 0.04 ]
audience_score 0.00 0.05 230 0.963 [ -0.13 , 0.13 ]
As indicated in Figure 57, Having introduced each of the variables and created new ones, twelve independent variables were selected for this next stage bivariate analysis and they are listed in Table 30. Table 30: Candidate predictors
Variable Description
thtr_rel_season Season the movie was released in theaters
director_experience Total number of films in sample for a director
cast_experience The sum across all cast members for a film, of the number of films in which each actor appeared
cast_votes Total number of allocated IMDB votes for the cast of a film
cast_votes_log Log of the total number of allocated IMDB votes for the cast of a film
scores 10 * IMDB Rating + critics score + audience_score
scores_log Log(10 * IMDB Rating + critics score + audience_score)
votes_imdb_rating Votes * imdb_rating
votes_imdb_rating_log log(votes * imdb_rating)
votes_critics_score votes * critics_score
votes_critics_score_log log(votes * critics_score)
votes_audience_score votes * audience_score
votes_audience_score_log log(votes * audience_score)
votes_scores votes * scores
votes_scores_log log(votes * scores)
genre Genre of movie (Action & Adventure, Comedy, Documentary, Drama, Horror, Mystery & Suspense, Other)
mpaa_rating MPAA rating of the movie (G, PG, PG-13, R, Unrated)
studio Studio that produced the movie
director Director of the movie
thtr_rel_month Month the movie is released in theaters
imdb_num_votes Number of votes on IMDB
imdb_num_votes_log Log number of IMDB votes
imdb_rating Rating on IMDB
critics_score Critics score on Rotten Tomatoes
audience_score Audience score on Rotten Tomatoes
best_pic_nom Whether or not the movie was nominated for a best picture Oscar (no, yes)
best_pic_win Whether or not the movie won a best picture Oscar (no, yes)
best_actor_win Whether or not one of the main actors in the movie ever won an Oscar (no, yes) – note that this is not necessarily whether the actor won an Oscar for their role in the given movie
best_actress_win Whether or not one of the main actresses in the movie ever won an Oscar (no, yes) – not that this is not necessarily whether the actresses won an Oscar for their role in the given movie
best_dir_win Whether or not the director of the movie ever won an Oscar (no, yes) – not that this is not necessarily whether the director won an Oscar for the given movie
top200_box Whether or not the movie is in the Top 200 Box Office list on BoxOfficeMojo (no, yes)
box_office Box office revenue from BoxOfficeMojo.com
box_office_log Log of Box office revenue from BoxOfficeMojo.com

Certain variables such as website addresses, film titles and runtimes provided no popularity predictive value. Similarly, studio, director, and actor variables were excluded in favor of their popularity and experience measures. The day of theatrical release as well as DVD release dates were not of interest for this analysis. Categorical scoring variables were excluded in favor of numeric measures. Lastly, dichotomous variables such as the oscar wins and inclusion in the box off top 200 provided insufficient sample size for one (or more) of these levels, as such they were excluded.

Genre

The hypothesis for the association between genre and movie popularity was as follows:
\(H_0\):


Part 4: Modeling

To ascertain the suitability of a candidate predictor, statistical inference (i.e., hypothesis testing) was conducted to draw conclusions about how movie popularity relates to various factors, based on the sample of popularity and the explanatory values.

The relationship between movie popularity and an explanatory variable can be described by the equation \(Y=β0+β1x\) where:
\(Y\) is the movie popularity score
\(β0\) is the \(y\)-intercept of the regression line
\(β1\) is the slope of the regression line
\(x\) is the coded value for the title type
The following analysis is only interested in the statistical significance of the slope, \(β1\), whereas \(β1 \neq 0\) indicates that the explanatory variable \(x\) can be used to predict \(Y\), movie popularity.

Before making any inferences, the conditions for inference were checked. For categorical variables, linearity, independence of errors, normality of errors, and equal error variance was checked. Next, hypotheses statements were tested whereby \(H_0\): \(β1 = 0\) and \(H_a\): \(β1 \neq 0\). The confidence level for all tests was 95%, with a two-tailed \(\alhha = 0.05\). Two test statistics were used: (1) the \(t\)-statistic and (2) the \(F\) statistic for analysis of variance.

Observations included/omitted - title_type == TV removed

Table 31: Forward Selection Prediction Model

Table 32: Backward Elimination Prediction Model


Part 5: Prediction

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Part 6: Conclusion

Appendix

Appendix A: Codebook

Table 33: Movie data set codebook
Source Type Variable Description
General
IMDB/RT/BO Categorical title Title of movie
IMDB/RT/BO Categorical imdb_url Link to IMDB page for the movie
IMDB/RT/BO Categorical rt_url Link to Rotten Tomatoes page for the movie
IMDB/RT/BO Categorical actor1 First main actor/actress in the abridged cast of the movie
IMDB/RT/BO Categorical actor2 Second main actor/actress in the abridged cast of the movie
IMDB/RT/BO Categorical actor3 Third main actor/actress in the abridged cast of the movie
IMDB/RT/BO Categorical actor4 Fourth main actor/actress in the abridged cast of the movie
Organization
IMDB/RT/BO Categorical actor5 Fifth main actor/actress in the abridged cast of the movie
IMDB/RT/BO Categorical thtr_rel_year Year the movie is released in theaters
IMDB/RT/BO Categorical thtr_rel_day Day of the month the movie is released in theaters
IMDB/RT/BO Categorical dvd_rel_year Year the movie is released on DVD
IMDB/RT/BO Categorical dvd_rel_month Month the movie is released on DVD
IMDB/RT/BO Categorical dvd_rel_day Day of the month the movie is released on DVD
IMDB/RT/BO Categorical critics_rating Categorical variable for critics rating on Rotten Tomatoes (Certified Fresh, Fresh, Rotten)
Dates
IMDB/RT/BO Categorical audience_rating Categorical variable for audience rating on Rotten Tomatoes (Spilled, Upright)
Derived Categorical thtr_rel_season Season the movie was released in theaters
Derived Numeric director_experience Total number of films in sample for a director
Derived Numeric cast_experience The sum across all cast members for a film, of the number of films in which each actor appeared
Derived Numeric cast_votes Total number of allocated IMDB votes for the cast of a film
Derived Numeric cast_votes_log Log of the total number of allocated IMDB votes for the cast of a film
Derived Numeric scores 10 * IMDB Rating + critics score + audience_score
Experience
Derived Numeric scores_log Log(10 * IMDB Rating + critics score + audience_score)
Derived Numeric votes_imdb_rating Votes * imdb_rating
Performance
Derived Numeric votes_imdb_rating_log log(votes * imdb_rating)
Derived Numeric votes_critics_score votes * critics_score
Derived Numeric votes_critics_score_log log(votes * critics_score)
Derived Numeric votes_audience_score votes * audience_score
Derived Numeric votes_audience_score_log log(votes * audience_score)
Derived Numeric votes_scores votes * scores
Derived Numeric votes_scores_log log(votes * scores)
IMDB/RT/BO Categorical title_type Type of movie (Documentary, Feature Film, TV Movie)
IMDB/RT/BO Categorical genre Genre of movie (Action & Adventure, Comedy, Documentary, Drama, Horror, Mystery & Suspense, Other)
IMDB/RT/BO Numeric runtime Runtime of movie (in minutes)
IMDB/RT/BO Categorical mpaa_rating MPAA rating of the movie (G, PG, PG-13, R, Unrated)
IMDB/RT/BO Categorical studio Studio that produced the movie
IMDB/RT/BO Categorical director Director of the movie
IMDB/RT/BO Categorical thtr_rel_month Month the movie is released in theaters
IMDB/RT/BO Numeric imdb_num_votes Number of votes on IMDB
Interaction
IMDB/RT/BO Numeric imdb_num_votes_log Log number of IMDB votes
IMDB/RT/BO Numeric imdb_rating Rating on IMDB
IMDB/RT/BO Numeric critics_score Critics score on Rotten Tomatoes
IMDB/RT/BO Numeric audience_score Audience score on Rotten Tomatoes
IMDB/RT/BO Categorical best_pic_nom Whether or not the movie was nominated for a best picture Oscar (no, yes)
IMDB/RT/BO Categorical best_pic_win Whether or not the movie won a best picture Oscar (no, yes)
IMDB/RT/BO Categorical best_actor_win Whether or not one of the main actors in the movie ever won an Oscar (no, yes) – note that this is not necessarily whether the actor won an Oscar for their role in the given movie
IMDB/RT/BO Categorical best_actress_win Whether or not one of the main actresses in the movie ever won an Oscar (no, yes) – not that this is not necessarily whether the actresses won an Oscar for their role in the given movie
IMDB/RT/BO Categorical best_dir_win Whether or not the director of the movie ever won an Oscar (no, yes) – not that this is not necessarily whether the director won an Oscar for the given movie
IMDB/RT/BO Categorical top200_box Whether or not the movie is in the Top 200 Box Office list on BoxOfficeMojo (no, yes)
Box Office
IMDB/RT/BO Numeric box_office Box office revenue from BoxOfficeMojo.com
IMDB/RT/BO Numeric box_office_log Log of Box office revenue from BoxOfficeMojo.com

Appendix B: Response Selection

Studio Experience

Figure 58: Log box office by studio experience regression line

Figure 59: Log box office by studio experience regression diagnostic plots

Appendix D: Bivariate Analysis Part II

Appendix E: Multivariate Analysis

References

John James jjames@datasciencesalon.org

13 November, 2017